TY - JOUR
T1 - Modelling continuum intensity perturbations caused by solar acoustic oscillations
AU - Kostogryz, N. M.
AU - Fournier, D.
AU - Gizon, L.
N1 - Funding Information:
Acknowledgements. We are thankful to Veronika Witzke for providing us with the MPS-ATLAS code for opacity calculation, Vincent Böning for providing us with the ADIPLS eigenfunctions, as well as Aaron Birch, Jesper Schou and Alexander Shapiro for useful discussions. This work was supported in part by a Max Planck Society grant “Preparations for PLATO Science” and German Aerospace Center (DLR) grants “PLATO Data Center” 50OO1501 and 50OP1902. LG and DF acknowledge partial support from ERC Synergy Grant WHOLE SUN 810218 and Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1456/432680300 Mathematics of Experiment, project C04.
Publisher Copyright:
© N. M. Kostogryz et al. 2021.
PY - 2021/10/1
Y1 - 2021/10/1
N2 - Context. Helioseismology is the study of the Sun's interior using observations of oscillations at the surface. It suffers from systematic errors, for instance a center-to-limb error in travel-time measurements. Understanding these errors requires an adequate understanding of the nontrivial relationship between wave displacement and helioseismic observables (intensity or velocity). Aims. The wave displacement causes perturbations in the atmospheric thermodynamical quantities which, in turn, perturb the opacity, the optical depth, the source function, and the local ray geometry, thus affecting the emergent intensity. We aim to establish the most complete relationship achieved to date between the wave displacement and the emergent intensity perturbation by solving the radiative transfer problem in the perturbed atmosphere. Methods. We derived an expression for the emergent intensity perturbation caused by acoustic oscillations at any point on the solar disk by applying a first-order perturbation theory. As input perturbations, we considerd adiabatic modes of oscillation of different degrees in a spherically-symmetric solar model. The background and the perturbed intensities are computed by solving the radiative transfer equation considering the main sources of opacity in the continuum (absorption and scattering). Results. We find that for all modes, the perturbations to the thermodynamical quantities are not sufficient to model the intensity perturbations: the geometrical effects due to the wave displacement must always be taken into account as they lead to a difference in amplitude and a phase shift between temperature perturbations at the surface and emergent intensity perturbations. The closer to the limb, the greater the differences. For modes with eigenfrequencies around 3 mHz, we found that the radial and horizontal components of the wave displacement are important, in particular, for high-degree modes. Conclusions. This work presents improvements for the computation of the intensity perturbations, in particular, for high-degree modes. Here, we explain the differences in intensity computations seen in earlier works. The phase shifts and amplitude differences between the temperature and intensity perturbations increase toward the limb. This should prove helpful when interpreting some of the systematic centre-to-limb effects observed in local helioseismology. The computations are fast (3 s for 2000 positions and one frequency for one core) and can be parallelised. This work can be extended to models of the line-of-sight velocity observable.
AB - Context. Helioseismology is the study of the Sun's interior using observations of oscillations at the surface. It suffers from systematic errors, for instance a center-to-limb error in travel-time measurements. Understanding these errors requires an adequate understanding of the nontrivial relationship between wave displacement and helioseismic observables (intensity or velocity). Aims. The wave displacement causes perturbations in the atmospheric thermodynamical quantities which, in turn, perturb the opacity, the optical depth, the source function, and the local ray geometry, thus affecting the emergent intensity. We aim to establish the most complete relationship achieved to date between the wave displacement and the emergent intensity perturbation by solving the radiative transfer problem in the perturbed atmosphere. Methods. We derived an expression for the emergent intensity perturbation caused by acoustic oscillations at any point on the solar disk by applying a first-order perturbation theory. As input perturbations, we considerd adiabatic modes of oscillation of different degrees in a spherically-symmetric solar model. The background and the perturbed intensities are computed by solving the radiative transfer equation considering the main sources of opacity in the continuum (absorption and scattering). Results. We find that for all modes, the perturbations to the thermodynamical quantities are not sufficient to model the intensity perturbations: the geometrical effects due to the wave displacement must always be taken into account as they lead to a difference in amplitude and a phase shift between temperature perturbations at the surface and emergent intensity perturbations. The closer to the limb, the greater the differences. For modes with eigenfrequencies around 3 mHz, we found that the radial and horizontal components of the wave displacement are important, in particular, for high-degree modes. Conclusions. This work presents improvements for the computation of the intensity perturbations, in particular, for high-degree modes. Here, we explain the differences in intensity computations seen in earlier works. The phase shifts and amplitude differences between the temperature and intensity perturbations increase toward the limb. This should prove helpful when interpreting some of the systematic centre-to-limb effects observed in local helioseismology. The computations are fast (3 s for 2000 positions and one frequency for one core) and can be parallelised. This work can be extended to models of the line-of-sight velocity observable.
KW - Methods: numerical
KW - Radiative transfer
KW - Sun: helioseismology
KW - Sun: oscillations
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U2 - 10.1051/0004-6361/202040264
DO - 10.1051/0004-6361/202040264
M3 - Article
AN - SCOPUS:85116457229
SN - 0004-6361
VL - 654
JO - Astronomy and Astrophysics
JF - Astronomy and Astrophysics
M1 - A1
ER -